Sunday, January 29, 2012

Minimalist Theory: One investment is not maximum*, and we don’t even know if it is optimal*, but it is better.


Minimalist Theory: One investment is not maximum*, and we don’t even know if it is optimal*, but it is better. I just made that up. But I sold 737.499 shares of MMPAX on 7/21 and 22 for a weighted average price of $12.88 per share for a total of $9,500. If I had not sold those shares, they would be worth $8392.74. So as of today, I am better off by $1107.26. With that $9500 I can buy back MMPAX for $11.38 per share.  That will buy me 834.80 shares.  If and when the price goes back up to $12.88 my 834.8 shares will be worth $10,752.22, which would yield me a profit of $1252.22. That’s minimalist. It’s not maximum because I could have potentially sold at a higher price. I could probably buy it back at a lower price. It is not the maximum of anything. My choices are not optimums either. But they are better choices. They are better than the alternative of not having done them, and I am better off, having done them. Maximizing value is an acceptable objective in investing, but it is not often obtainable. Optimizing value is more realistic in terms of choosing the best alternative, but as investors we do not know all the possible choices. In my case, all I know is a dichotomy: do it or don’t do it. First: either sell if or hold it. Second: either hold the cash or buy the stock back. After selling the 737.499 shares and getting the $9500, I watched the market fall. I was better off because I no longer held these shares, which had dropped in value. If I just hold the cash, I am better off by $1107.26. I can stop here in the analysis, because the rest is based on going forward in time and making an investment decision no different than any other. However, if the price recovered after I buy back the shares, I can increase my relative value to $1252.22. That’s not the best decision I could have made. It is not the optimum from the choices that had been available, in hindsight. But it is better. Investors do not shoot for maximums or even optimums. They do not win 90% of the time or even 80 or 70%. I only really have to win 51% of the time. (“In this business if you're good, you're right six times out of ten. You're never going to be right nine times out of ten.” Peter Lynch.  I also did not invest the maximum amount of money and do not know if it was optimum. I make myself happy with small gains. And they are a lot better than losses.

Do you know the difference between maximum and optimum? In mathematics, the maximum and minimum (plural: maxima and minima) of a function, known collectively as extrema (singular: extremum), are the largest and smallest value that the function takes at a point either within a given neighborhood (local or relative extremum) or on the function domain in its entirety (global or absolute extremum).

More generally, the maximum and minimum of a set (as defined in set theory) are the greatest and least element in the set. Unbounded infinite sets such as the set of real numbers have no minimum and maximum.

In mathematics and computational science, mathematical optimization (alternatively, optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives.

In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

Frequent Flyer’s Tip: The best fares are probably available on Friday the 13th and days like that. Also I noticed December and June all the fares are higher. But I don’t know that much. You other guys know a lot more about flying than I do.

Invest in Sugar, I guess: I just saw an ad for General Mills Kids Cereals. Those are the ones that have the mega-sugar-doses. Why is it we do that to our kids? Oh maybe it’s just my imagination! We couldn’t possibly give them food that is 1/3 highly refined white sugars to start their little days, could we?

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